Multiplying a sine or cosine function by a constant changes the graph of the parent function
; specifically, you change the amplitude of the graph. When measuring the height of a graph, you measure the distance between the maximum crest and the minimum wave.
How do you change a sine wave?
You can move a sine curve up or down
by simply adding or subtracting a number from the equation of the curve
. For example, the graph of y = sin x + 4 moves the whole curve up 4 units, with the sine curve crossing back and forth over the line y = 4.
What is amplitude of a sine wave?
The amplitude of the sine function is
the distance from the middle value or line running through the graph up to the highest point
. In other words, the amplitude is half the distance from the lowest value to the highest value.
How do you find the amplitude of a sine wave?
Amplitude is the distance between the center line of the function and the top or bottom of the function, and the period is the distance between two peaks of the graph, or the distance it takes for the entire graph to repeat. Using this equation:
Amplitude =APeriod =2πBHorizontal shift to the left =CVertical shift =D
.
How do you change amplitude?
The amplitude of a sound is controlled by
multiplying the sound wave by a certain factor
. A multiplier of 1 represents “unity gain”, meaning no change. Multiplying by a factor between 0 and 1 reduces the amplitude of the sound.
How does amplitude affect a sine graph?
Clearly we can see the affect a has on the graph y = a sin (bx + c). When 0 < a < 1,
the amplitude of the graph decreases
, causing the slopes of the graph to appear more “flat”. … Changing the a from positive to negative reflects the graph across the x-axis.
What does a sine graph look like?
To graph the sine function, we mark the angle along the horizontal x axis, and for each angle, we put the sine of that angle on the vertical y-axis. The result, as seen above, is
a smooth curve that varies from +1 to -1
. Curves that follow this shape are called ‘sinusoidal’ after the name of the sine function.
What is the formula for a sine wave?
Sine Wave. … A general form of a sinusoidal wave is
y(x,t)=Asin(kx−ωt+φ) y ( x , t ) = A sin ( kx − ω t + φ )
, where A is the amplitude of the wave, ω is the wave’s angular frequency, k is the wavenumber, and φ is the phase of the sine wave given in radians.
Why is sine wave preferred?
The sine wave is important in physics
because it retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude
. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.
Is light a sine wave?
Waves can take on many shapes. One of the most common wave shapes is called a sine wave, shown below. Light waves are
one of many types of waves in nature shaped
like sine waves.
What does amplitude do to a graph?
Technically, the amplitude is
the absolute value of whatever is multiplied on the trig function
. The amplitude just says how “tall” or “short” the curve is; it’s up to you to notice whether there’s a “minus” on that multiplier, and thus whether or not the function is in the usual orientation, or upside-down.
How do you find amplitude?
The Amplitude is
the height from the center line to the peak
(or to the trough). Or we can measure the height from highest to lowest points and divide that by 2.
What is the frequency of a sine wave?
The frequency of a sine wave is
the number of complete cycles that happen every second
. (A cycle is the same as the period, see below.) In the bouncing weight above, the frequency is about one cycle per second. In this formula the frequency is w.
How do you increase the amplitude of a wave?
Amplitude is the size of the wave, or the vertical distance between its peak and it’s trough. Therefore,
by making larger motions
, you increase the amplitude. The other property is frequency, which is the distance from one peak/trough to the next.
Which letter affects the amplitude of a graph?
The letter A
represents the amplitude of the sine or cosine function, and it affects the steepness or flatness of the graphs of any of the trig functions. If the absolute value (ignore the + or – sign) of A is some number greater than 1, then the graph is steeper than usual.
Can the amplitude of a sine graph be negative?
The difference with a negative value of a however, is
our sine curve now has a negative amplitude
. In other words, our graphs are the same as when a was a positive value, but are now reflected across the x-axis. … Notice how different values of a change the amplitude of our sine curve.
